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Transition Year Maths


Example 2: Write the following numbers without scientific notation: (a) 4·4 × 100 (b) 4·4 × 101 (c) 4·4 × 102 (d) 4·4 × 103 (e) 4·4 × 104 (f) 4·4 × 105


= . . . . . 4·4 (g) 4·4 × 100 = . . . . . . 44 (h) 4·4 × 10-1 = . . . . . 440 (i) 4·4 × 10-2 (j) 4·4 × 10-3


= . . . 4,400


= . . 44,000 (k) 4·4 × 10-4 = . 440,000 (l) 4·4 × 10-5


= . . . . . . . . . . 4·4 = . . . . . . . . . 0·44 = . . . . . . . . 0·044 = . . . . . . . 0·0044 = . . . . . . 0·00044 = . . . . . 0·000044


In this book calculations can be done with and without a calculator. However, a calculator makes some calculations very easy.


Adding: Add 3·2 × 103 and 1·4 × 104


Using the rule above, bring both numbers to the same power and add as normal. 3·2 × 103 +1·4 × 104


= or using a calculator


3 · 2 EXP 3 + 1 · 4 EXP 4 =


Multiplying: Multiply 3·2 × 103 ∴ 3·2 × 103 by 1·4 × 104


3·2 by 1·4 = 4·48 103


by 104 = 107 (add power) × 1·4 × 104 or using a calculator


3 · 2 EXP 3 × 1 · 4 EXP 4 =


Subtraction: Take 1·4 × 104


. . . . . . . . . . . . 44,800,000 = 4·48 × 107 . . . . . . . . . . . . 17,200 ·32 × 104


+1·4 × 104 1·72 × 104


. . . . . . . . . .


from 3·2 × 105


Using the rule above, bring both powers to same power and subtract as normal. 3·2 × 105 –1·4 × 104


= 3·2 × 105 = –0·14 × 105 3·06 × 105


or using a calculator


3 · 2 EXP 5 – 1 · 4 EXP 4 =


. . . . . . . . . . . . 306,000 (move decimal once to left, power goes up 1)


8


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